Grades 3-4 Video Solutions 2021-video 2021 3-4/20

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Problem number 20. Mia throws darts at balloons worth 3, 9, 13, 14, and 18 points. She scores 30 points in total. Which balloon does Mia definitely hit?  A, 3, B, 9, C, 13, D, 14, E, 18. We don't know how many balloons Mia hit, so we just need to look at the numbers  and find all the possible ways that we can make a sum of 30 out of them. I find it easiest to start with the largest number because that will easily eliminate some possibilities.  So if we start with 18, we need to add 30 minus 18, 12 more to make 30.  Now we can make 12 by adding 3 and 9. So 18 plus 3 plus 9 will give us 30. So that's one option that she hit the balloons of the 18, 3, and 9.  And that's the only way we can make 30 points using the number 18.  So now let's start with 14.  30 minus 14 is 16. We can make 16 out of these balloons only by adding 3 and 13 to it.  So we have 14, again, 3, and 13.  If we use the 13, we have the option we just made.  30 minus 13 is 17, and the only way we have to make 17 using these balloons is what we already had with the 14 and the 3.  So these two options are the same.  If we use the 9, we need to add 21 to it.  And the only way we will get 21 is by adding together 3 and 18,  as we had done in the first step.  If we use 3, we need to add 27 to it. We already used two options because both of the sets of 30s that we made had a 3 in it, and we don't have another way to make 27.  So again, we've already listed all the options that use the 3.  So there are only two options for the balloons which Mia hit to make 30.  She either hit 18, 3, and 9, or she hit 14, 3, and 13. In either case, the balloon with the 3 is one that she hit.  So our answer is A, 3.

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